Three Views of Logic: Mathematics, Philosophy, and Computer Science
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton
Princeton University Press
2014
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Print version record. - 9.9 Intuitive Descriptions of the Four-Valued Logic Semantics |
| Beschreibung: | 1 online resource (339 pages) |
| ISBN: | 0691160449 1306282594 140084875X 9780691160443 9781306282598 9781400848751 |
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| 505 | 8 | |a Cover; Title; Copyright; Contents; Preface; Acknowledgments; PART 1. Proof Theory; 1 Propositional Logic; 1.1 Propositional Logic Semantics; 1.2 Syntax: Deductive Logics; 1.3 The Resolution Formal Logic; 1.4 Handling Arbitrary Propositional Wffs; 2 Predicate Logic; 2.1 First-Order Semantics; 2.2 Resolution for the Predicate Calculus; 2.2.1 Substitution; 2.2.2 The Formal System for Predicate Logic; 2.2.3 Handling Arbitrary Predicate Wffs; 3 An Application: Linear Resolution and Prolog; 3.1 OSL-Resolution; 3.2 Horn Logic; 3.3 Input Resolution and Prolog; Appendix A: The Induction Principle | |
| 505 | 8 | |a Appendix B: First-Order ValuationAppendix C: A Commentary on Prolog; References; PART 2. Computability Theory; 4 Overview of Computability; 4.1 Decision Problems and Algorithms; 4.2 Three Informal Concepts; 5 A Machine Model of Computability; 5.1 Register Machines and RM-Computable Functions; 5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions; 5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem; 5.4 Unsolvability of Hilbert's Decision Problem and Thue's Word Problem; 6 A Mathematical Model of Computability | |
| 505 | 8 | |a 6.1 Recursive Functions and the Church-Turing Thesis6.2 Recursive Relations and RE Relations; 6.3 Primitive Recursive Functions and Relations; Coding; 6.4 Kleene Computation Relation Tn(e, a1 ..., an, c); 6.5 Partial Recursive Functions; Enumeration Theorems; 6.6 Computability and the Incompleteness Theorem; List of Symbols; References; PART 3. Philosophical Logic; 7 Non-Classical Logics; 7.1 Alternatives to Classical Logic vs. Extensions of Classical Logic; 7.2 From Classical Logic to Relevance Logic; 7.2.1 The (So-Called) "Paradoxes of Implication." | |
| 505 | 8 | |a 7.2.2 Material Implication and Truth Functional Connectives7.2.3 Implication and Relevance; 7.2.4 Revisiting Classical Propositional Calculus: What to Save, What to Change, What to Add?; 8 Natural Deduction: Classical and Non-Classical; 8.1 Fitch's Natural Deduction System for Classical Propositional Logic; 8.2 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Necessity; 8.3 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Relevance; 8.4 The Rules of System FE (Fitch-Style Formulation of the Logic of Entailment) | |
| 505 | 8 | |a 8.5 The Connective "Or," Material Implication, and the Disjunctive Syllogism9 Semantics for Relevance Logic: A Useful Four-Valued Logic; 9.1 Interpretations, Valuations, and Many Valued Logics; 9.2 Contexts in Which This Four-Valued Logic Is Useful; 9.3 The Artificial Reasoner's (Computer's) "State of Knowledge"; 9.4 Negation in This Four-Valued Logic; 9.5 Lattices: A Brief Tutorial; 9.6 Finite Approximation Lattices and Scott's Thesis; 9.7 Applying Scott's Thesis to Negation, Conjunction, and Disjunction; 9.8 The Logical Lattice L4 | |
| 505 | 8 | |a Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and fir | |
| 650 | 4 | |a Computable functions | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Mathematics / Philosophy | |
| 650 | 4 | |a Nonclassical mathematical logic | |
| 650 | 4 | |a Proof theory | |
| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Linear & Nonlinear Programming |2 bisacsh | |
| 650 | 7 | |a Computable functions |2 fast | |
| 650 | 7 | |a Nonclassical mathematical logic |2 fast | |
| 650 | 7 | |a Proof theory |2 fast | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Philosophie | |
| 650 | 4 | |a Proof theory | |
| 650 | 4 | |a Computable functions | |
| 650 | 4 | |a Nonclassical mathematical logic | |
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Datensatz im Suchindex
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| author | Loveland, Donald W. 1934- |
| author_GND | (DE-588)104961139X (DE-588)1049612272 |
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| author_sort | Loveland, Donald W. 1934- |
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| bvnumber | BV043032709 |
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| contents | Cover; Title; Copyright; Contents; Preface; Acknowledgments; PART 1. Proof Theory; 1 Propositional Logic; 1.1 Propositional Logic Semantics; 1.2 Syntax: Deductive Logics; 1.3 The Resolution Formal Logic; 1.4 Handling Arbitrary Propositional Wffs; 2 Predicate Logic; 2.1 First-Order Semantics; 2.2 Resolution for the Predicate Calculus; 2.2.1 Substitution; 2.2.2 The Formal System for Predicate Logic; 2.2.3 Handling Arbitrary Predicate Wffs; 3 An Application: Linear Resolution and Prolog; 3.1 OSL-Resolution; 3.2 Horn Logic; 3.3 Input Resolution and Prolog; Appendix A: The Induction Principle Appendix B: First-Order ValuationAppendix C: A Commentary on Prolog; References; PART 2. Computability Theory; 4 Overview of Computability; 4.1 Decision Problems and Algorithms; 4.2 Three Informal Concepts; 5 A Machine Model of Computability; 5.1 Register Machines and RM-Computable Functions; 5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions; 5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem; 5.4 Unsolvability of Hilbert's Decision Problem and Thue's Word Problem; 6 A Mathematical Model of Computability 6.1 Recursive Functions and the Church-Turing Thesis6.2 Recursive Relations and RE Relations; 6.3 Primitive Recursive Functions and Relations; Coding; 6.4 Kleene Computation Relation Tn(e, a1 ..., an, c); 6.5 Partial Recursive Functions; Enumeration Theorems; 6.6 Computability and the Incompleteness Theorem; List of Symbols; References; PART 3. Philosophical Logic; 7 Non-Classical Logics; 7.1 Alternatives to Classical Logic vs. Extensions of Classical Logic; 7.2 From Classical Logic to Relevance Logic; 7.2.1 The (So-Called) "Paradoxes of Implication." 7.2.2 Material Implication and Truth Functional Connectives7.2.3 Implication and Relevance; 7.2.4 Revisiting Classical Propositional Calculus: What to Save, What to Change, What to Add?; 8 Natural Deduction: Classical and Non-Classical; 8.1 Fitch's Natural Deduction System for Classical Propositional Logic; 8.2 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Necessity; 8.3 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Relevance; 8.4 The Rules of System FE (Fitch-Style Formulation of the Logic of Entailment) 8.5 The Connective "Or," Material Implication, and the Disjunctive Syllogism9 Semantics for Relevance Logic: A Useful Four-Valued Logic; 9.1 Interpretations, Valuations, and Many Valued Logics; 9.2 Contexts in Which This Four-Valued Logic Is Useful; 9.3 The Artificial Reasoner's (Computer's) "State of Knowledge"; 9.4 Negation in This Four-Valued Logic; 9.5 Lattices: A Brief Tutorial; 9.6 Finite Approximation Lattices and Scott's Thesis; 9.7 Applying Scott's Thesis to Negation, Conjunction, and Disjunction; 9.8 The Logical Lattice L4 Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and fir |
| ctrlnum | (OCoLC)867317379 (DE-599)BVBBV043032709 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043032709 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:31Z |
| institution | BVB |
| isbn | 0691160449 1306282594 140084875X 9780691160443 9781306282598 9781400848751 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028457358 |
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| open_access_boolean | |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (339 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Princeton University Press |
| record_format | marc |
| spelling | Loveland, Donald W. 1934- Verfasser (DE-588)104961139X aut Three Views of Logic Mathematics, Philosophy, and Computer Science Princeton Princeton University Press 2014 1 online resource (339 pages) txt rdacontent c rdamedia cr rdacarrier Print version record. - 9.9 Intuitive Descriptions of the Four-Valued Logic Semantics Cover; Title; Copyright; Contents; Preface; Acknowledgments; PART 1. Proof Theory; 1 Propositional Logic; 1.1 Propositional Logic Semantics; 1.2 Syntax: Deductive Logics; 1.3 The Resolution Formal Logic; 1.4 Handling Arbitrary Propositional Wffs; 2 Predicate Logic; 2.1 First-Order Semantics; 2.2 Resolution for the Predicate Calculus; 2.2.1 Substitution; 2.2.2 The Formal System for Predicate Logic; 2.2.3 Handling Arbitrary Predicate Wffs; 3 An Application: Linear Resolution and Prolog; 3.1 OSL-Resolution; 3.2 Horn Logic; 3.3 Input Resolution and Prolog; Appendix A: The Induction Principle Appendix B: First-Order ValuationAppendix C: A Commentary on Prolog; References; PART 2. Computability Theory; 4 Overview of Computability; 4.1 Decision Problems and Algorithms; 4.2 Three Informal Concepts; 5 A Machine Model of Computability; 5.1 Register Machines and RM-Computable Functions; 5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions; 5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem; 5.4 Unsolvability of Hilbert's Decision Problem and Thue's Word Problem; 6 A Mathematical Model of Computability 6.1 Recursive Functions and the Church-Turing Thesis6.2 Recursive Relations and RE Relations; 6.3 Primitive Recursive Functions and Relations; Coding; 6.4 Kleene Computation Relation Tn(e, a1 ..., an, c); 6.5 Partial Recursive Functions; Enumeration Theorems; 6.6 Computability and the Incompleteness Theorem; List of Symbols; References; PART 3. Philosophical Logic; 7 Non-Classical Logics; 7.1 Alternatives to Classical Logic vs. Extensions of Classical Logic; 7.2 From Classical Logic to Relevance Logic; 7.2.1 The (So-Called) "Paradoxes of Implication." 7.2.2 Material Implication and Truth Functional Connectives7.2.3 Implication and Relevance; 7.2.4 Revisiting Classical Propositional Calculus: What to Save, What to Change, What to Add?; 8 Natural Deduction: Classical and Non-Classical; 8.1 Fitch's Natural Deduction System for Classical Propositional Logic; 8.2 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Necessity; 8.3 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Relevance; 8.4 The Rules of System FE (Fitch-Style Formulation of the Logic of Entailment) 8.5 The Connective "Or," Material Implication, and the Disjunctive Syllogism9 Semantics for Relevance Logic: A Useful Four-Valued Logic; 9.1 Interpretations, Valuations, and Many Valued Logics; 9.2 Contexts in Which This Four-Valued Logic Is Useful; 9.3 The Artificial Reasoner's (Computer's) "State of Knowledge"; 9.4 Negation in This Four-Valued Logic; 9.5 Lattices: A Brief Tutorial; 9.6 Finite Approximation Lattices and Scott's Thesis; 9.7 Applying Scott's Thesis to Negation, Conjunction, and Disjunction; 9.8 The Logical Lattice L4 Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and fir Computable functions Logic, Symbolic and mathematical Mathematics / Philosophy Nonclassical mathematical logic Proof theory MATHEMATICS / General bisacsh MATHEMATICS / Linear & Nonlinear Programming bisacsh Computable functions fast Nonclassical mathematical logic fast Proof theory fast Mathematik Philosophie Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Nichtklassische Logik (DE-588)4197462-1 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s Berechenbarkeit (DE-588)4138368-0 s Nichtklassische Logik (DE-588)4197462-1 s 1\p DE-604 Hodel, Richard E. Sonstige (DE-588)1049612272 oth Sterrett, Susan G. Sonstige oth Erscheint auch als Druck-Ausgabe Loveland, Donald W . Three Views of Logic : Mathematics, Philosophy, and Computer Science http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=639113 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Loveland, Donald W. 1934- Three Views of Logic Mathematics, Philosophy, and Computer Science Cover; Title; Copyright; Contents; Preface; Acknowledgments; PART 1. Proof Theory; 1 Propositional Logic; 1.1 Propositional Logic Semantics; 1.2 Syntax: Deductive Logics; 1.3 The Resolution Formal Logic; 1.4 Handling Arbitrary Propositional Wffs; 2 Predicate Logic; 2.1 First-Order Semantics; 2.2 Resolution for the Predicate Calculus; 2.2.1 Substitution; 2.2.2 The Formal System for Predicate Logic; 2.2.3 Handling Arbitrary Predicate Wffs; 3 An Application: Linear Resolution and Prolog; 3.1 OSL-Resolution; 3.2 Horn Logic; 3.3 Input Resolution and Prolog; Appendix A: The Induction Principle Appendix B: First-Order ValuationAppendix C: A Commentary on Prolog; References; PART 2. Computability Theory; 4 Overview of Computability; 4.1 Decision Problems and Algorithms; 4.2 Three Informal Concepts; 5 A Machine Model of Computability; 5.1 Register Machines and RM-Computable Functions; 5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions; 5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem; 5.4 Unsolvability of Hilbert's Decision Problem and Thue's Word Problem; 6 A Mathematical Model of Computability 6.1 Recursive Functions and the Church-Turing Thesis6.2 Recursive Relations and RE Relations; 6.3 Primitive Recursive Functions and Relations; Coding; 6.4 Kleene Computation Relation Tn(e, a1 ..., an, c); 6.5 Partial Recursive Functions; Enumeration Theorems; 6.6 Computability and the Incompleteness Theorem; List of Symbols; References; PART 3. Philosophical Logic; 7 Non-Classical Logics; 7.1 Alternatives to Classical Logic vs. Extensions of Classical Logic; 7.2 From Classical Logic to Relevance Logic; 7.2.1 The (So-Called) "Paradoxes of Implication." 7.2.2 Material Implication and Truth Functional Connectives7.2.3 Implication and Relevance; 7.2.4 Revisiting Classical Propositional Calculus: What to Save, What to Change, What to Add?; 8 Natural Deduction: Classical and Non-Classical; 8.1 Fitch's Natural Deduction System for Classical Propositional Logic; 8.2 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Necessity; 8.3 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Relevance; 8.4 The Rules of System FE (Fitch-Style Formulation of the Logic of Entailment) 8.5 The Connective "Or," Material Implication, and the Disjunctive Syllogism9 Semantics for Relevance Logic: A Useful Four-Valued Logic; 9.1 Interpretations, Valuations, and Many Valued Logics; 9.2 Contexts in Which This Four-Valued Logic Is Useful; 9.3 The Artificial Reasoner's (Computer's) "State of Knowledge"; 9.4 Negation in This Four-Valued Logic; 9.5 Lattices: A Brief Tutorial; 9.6 Finite Approximation Lattices and Scott's Thesis; 9.7 Applying Scott's Thesis to Negation, Conjunction, and Disjunction; 9.8 The Logical Lattice L4 Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and fir Computable functions Logic, Symbolic and mathematical Mathematics / Philosophy Nonclassical mathematical logic Proof theory MATHEMATICS / General bisacsh MATHEMATICS / Linear & Nonlinear Programming bisacsh Computable functions fast Nonclassical mathematical logic fast Proof theory fast Mathematik Philosophie Berechenbarkeit (DE-588)4138368-0 gnd Nichtklassische Logik (DE-588)4197462-1 gnd Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4138368-0 (DE-588)4197462-1 (DE-588)4145177-6 |
| title | Three Views of Logic Mathematics, Philosophy, and Computer Science |
| title_auth | Three Views of Logic Mathematics, Philosophy, and Computer Science |
| title_exact_search | Three Views of Logic Mathematics, Philosophy, and Computer Science |
| title_full | Three Views of Logic Mathematics, Philosophy, and Computer Science |
| title_fullStr | Three Views of Logic Mathematics, Philosophy, and Computer Science |
| title_full_unstemmed | Three Views of Logic Mathematics, Philosophy, and Computer Science |
| title_short | Three Views of Logic |
| title_sort | three views of logic mathematics philosophy and computer science |
| title_sub | Mathematics, Philosophy, and Computer Science |
| topic | Computable functions Logic, Symbolic and mathematical Mathematics / Philosophy Nonclassical mathematical logic Proof theory MATHEMATICS / General bisacsh MATHEMATICS / Linear & Nonlinear Programming bisacsh Computable functions fast Nonclassical mathematical logic fast Proof theory fast Mathematik Philosophie Berechenbarkeit (DE-588)4138368-0 gnd Nichtklassische Logik (DE-588)4197462-1 gnd Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Computable functions Logic, Symbolic and mathematical Mathematics / Philosophy Nonclassical mathematical logic Proof theory MATHEMATICS / General MATHEMATICS / Linear & Nonlinear Programming Mathematik Philosophie Berechenbarkeit Nichtklassische Logik Beweistheorie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=639113 |
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